The given problem provides a function $f(x) = \frac{150 - 20x}{x}$ and asks to find $f\left(\frac{2}{3}\right)$ and $f(-3)$.

Let's calculate these values step-by-step.

1. Calculate $f\left(\frac{2}{3}\right)$:

$f\left(\frac{2}{3}\right) = \frac{150 - 20\left(\frac{2}{3}\right)}{\frac{2}{3}}$ Simplify the numerator: $150 - 20\left(\frac{2}{3}\right) = 150 - \frac{40}{3} = \frac{450}{3} - \frac{40}{3} = \frac{410}{3}$

Now divide by $\frac{2}{3}$: $f\left(\frac{2}{3}\right) = \frac{\frac{410}{3}}{\frac{2}{3}} = \frac{410}{3} \times \frac{3}{2} = \frac{410}{2} = 205$

So, $f\left(\frac{2}{3}\right) = 205$.

2. Calculate $f(-3)$:

$f(-3) = \frac{150 - 20(-3)}{-3}$ Simplify the numerator: $150 - 20(-3) = 150 + 60 = 210$

Now divide by $-3$: $f(-3) = \frac{210}{-3} = -70$

So, $f(-3) = -70$.

Final Answers:

1. $f\left(\frac{2}{3}\right) = 205$
2. $f(-3) = -70$

Would you like more details on any of the steps or have additional questions?

Related Questions:

1. How do you simplify complex fractions step-by-step?
2. What are the properties of rational functions?
3. How do you find vertical and horizontal asymptotes of a function like $f(x)$?
4. What is the domain and range of the function $f(x) = \frac{150 - 20x}{x}$?
5. How do you determine critical points for $f(x)$?

Tip: Always check the domain of a function before calculating specific values, especially for rational functions where the denominator can be zero.